Reduce to lowest terms: $- \dfrac{3}{4} \div \dfrac{5}{9} = {?}$
Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $ \dfrac{5}{9}$ is $ \dfrac{9}{5}$ Therefore: $ - \dfrac{3}{4} \div \dfrac{5}{9} = - \dfrac{3}{4} \times \dfrac{9}{5} $ $ \phantom{- \dfrac{3}{4} \times \dfrac{9}{5}} = \dfrac{-3 \times 9}{4 \times 5} $ $ \phantom{- \dfrac{3}{4} \times \dfrac{9}{5}} = \dfrac{-27}{20} $